Thermodynamic Study of 1,4-Bis(3-methylimidazolium-1-yl)butane Bis(trifluoromethylsulfonyl)imide ([C4(MIm)2][NTf2]2) from 6 to 350 K

The molar heat capacity of 1,4-bis(3-methylimidazolium-1-yl)butane bis(trifluoromethylsulfonyl)imide dicationic ionic compound ([C4(MIm)2][NTf2]2) has been studied over the temperature range from 6 to 350 K by adiabatic calorimetry. In the above temperature interval, this compound has been found to form crystal, liquid, and supercooled liquid. For [C4(MIm)2][NTf2]2, the temperature of fusion T°fus = (337.88 ± 0.01) K has been determined by the fractional melting experiments, the enthalpy of fusion ΔfusH° = (52.79 ± 0.28) kJ mol−1 has been measured using the calorimetric method of continuous energy input, and the entropy of fusion ΔfusS° = (156.2 ± 1.7) J K−1 mol−1 has also been evaluated. The standard thermodynamic functions of the studied dicationic ionic compound, namely, the heat capacity Cp°(T), the enthalpy [H°(T) − H°(0)], the entropy S°(T) and the Gibbs free energy [G°(T) − H°(0)] have been calculated on the basis of the experimental data for the temperature range up to 350 K. The results have been discussed and compared with those available in the literature and in the NIST Ionic Liquids Database (ILThermo) for monocationic ionic compounds.


Introduction
The fields of interest in ionic liquids (ILs) include chemical synthesis and catalysis, pharmaceutics and medicine, electrochemistry, biomass conversion, fuel production and processing, liquid crystal development, material science, and many others [1][2][3].Since the beginnings of the "modern age" of research on ILs, the family of organic salts containing a 1,3-dialkyl imidazolium cation and the bis(trifluoromehtyl)sulfonylimide (NTf 2 ) anion has been one of most widely investigated among aprotic ILs [4][5][6][7], although more recently the research involving ILs has been mainly focused on greener compounds.This is in part due to the high thermal stability of these compounds, which is related to the scarce nucleophilicity of the anionic portion [8,9].Indeed, if the well-known low volatility of ILs is not accompanied by sufficiently high thermal stability, a number of potential applications of this wide class of compounds cannot be exploited.In the search for improved variants of classic alkylimidazolium NTf 2 ILs with lower volatility and good thermal stability at relatively high temperatures, ILs with a dipositive dication, such as that reported in Figure 1, were more recently considered (commonly known as dicationic ionic liquids, DILs) [10,11].In these compounds, the doubly charged cation contains two alkylimidazolium rings linked by a (CH 2 ) n chain, with n going typically from 1 to 10-12.It was recently shown that DILs have a number of peculiar physical and chemical properties compared to their monocationic counterparts [12].For example, imidazolium-based DILs exhibit a significant increase in the melting temperature, which can arise from π-π stacking.
Molecules 2024, 29, 4180 2 of 13 classic alkylimidazolium NTf2 ILs with lower volatility and good thermal stability at relatively high temperatures, ILs with a dipositive dication, such as that reported in Figure 1, were more recently considered (commonly known as dicationic ionic liquids, DILs) [10,11].In these compounds, the doubly charged cation contains two alkylimidazolium rings linked by a (CH2)n chain, with n going typically from 1 to 10-12.It was recently shown that DILs have a number of peculiar physical and chemical properties compared to their monocationic counterparts [12].For example, imidazolium-based DILs exhibit a significant increase in the melting temperature, which can arise from π-π stacking.Despite this interest, the thermodynamic characterization of DILs is presently very scarce in the literature.To the best of our knowledge, the only studies reported so far were focused on the evaporation of the compound with the n = 3 linker and a methyl group on the imidazolium rings [13,14].In particular, no study has been reported on the heat capacity of any member of this family, and no thermodynamic functions are presently available in both the condensed and vapor phases.Indeed, due to the lack of these data, the shifting of evaporation and sublimation enthalpies from the experimental temperatures to the reference temperature of 298.15K had to be carried out on the basis of empirical estimates, with a likely loss of accuracy.
In order to begin filling this gap, we present here the first experimental determination of the heat capacity of 1,4-bis(3-methylimidazolium-1-yl)butane bis(trifluoromethylsulfonyl)imide ([C4(MIm)2][NTf2]2) in the temperature range from 6 to 350 K by classic adiabatic calorimetry and we derive the thermodynamic functions therefrom.For the sake of comparison, the prototypical monocationic IL, [C4MIm][NTf2], whose heat capacity values are available in the literature in the entire temperature range [15], was also subjected to the same measurements.Previously, the results of NMR analysis for [C4(MIm)2][NTf2]2 were reported in [16].

Heat Capacity Measurements
In order to check the internal consistency of the results of adiabatic measurements, similar to what was reported in a recently published study [17], a set of the heat capacity values was collected for the prototypic 1-butyl-3-methylimidazolium bis(trifluoromethyl)sulfonylimide monocationic ionic liquid [C4MIm][NTf2] (Table S1, Supplementary Material) under the identical operative conditions used for the tested compound  Despite this interest, the thermodynamic characterization of DILs is presently very scarce in the literature.To the best of our knowledge, the only studies reported so far were focused on the evaporation of the compound with the n = 3 linker and a methyl group on the imidazolium rings [13,14].In particular, no study has been reported on the heat capacity of any member of this family, and no thermodynamic functions are presently available in both the condensed and vapor phases.Indeed, due to the lack of these data, the shifting of evaporation and sublimation enthalpies from the experimental temperatures to the reference temperature of 298.15K had to be carried out on the basis of empirical estimates, with a likely loss of accuracy.
In order to begin filling this gap, we present here the first experimental determination of the heat capacity of 1,4-bis(3-methylimidazolium-1-yl)butane bis(trifluoromethylsulfonyl)imide ([C 4 (MIm) 2 ][NTf 2 ] 2 ) in the temperature range from 6 to 350 K by classic adiabatic calorimetry and we derive the thermodynamic functions therefrom.For the sake of comparison, the prototypical monocationic IL, [C 4 MIm][NTf 2 ], whose heat capacity values are available in the literature in the entire temperature range [15], was also subjected to the same measurements.Previously, the results of NMR analysis for [C 4 (MIm) 2 ][NTf 2 ] 2 were reported in [16].

Heat Capacity Measurements
In order to check the internal consistency of the results of adiabatic measurements, similar to what was reported in a recently published study [17], a set of the heat capacity values was collected for the prototypic 1-butyl-3-methylimidazolium bis(trifluoromethyl)sulfonylimide monocationic ionic liquid  1 and Figure 2, respectively.The experimental C p values were fitted in all the temperature regions where any transformations are absent according to the following polynomial Equations ( 1)-(3): where A i is the fitting polynomial coefficient, and n is the number of coefficients (starting from 0).The corresponding fitting coefficients are listed in Table S2 (Supplementary Material).The relative deviation of the experimental data from the fitting values related to the tested compound is plotted in Figure S3 (Supplementary Material).
where Ai is the fitting polynomial coefficient, and n is the number of coefficients (starting from 0).The corresponding fitting coefficients are listed in Table S2 (Supplementary Material).The relative deviation of the experimental data from the fitting values related to the tested compound is plotted in Figure S3 (Supplementary Material).The sample of ionic compound [C4(MIm)2][NTf2]2 was cooled down from the room temperature (T~298.15K) to T~6 K by liquid helium.At the subsequent heating, the heat capacity of [C4(MIm)2][NTf2]2 gradually increases in the temperature range from T = (6 to 300) K.Then, the fusion of the studied compound was observed.The sample of ionic compound [C 4 (MIm) 2 ][NTf 2 ] 2 was cooled down from the room temperature (T~298.15K) to T~6 K by liquid helium.At the subsequent heating, the heat capacity of [C 4 (MIm) 2 ][NTf 2 ] 2 gradually increases in the temperature range from T = (6 to 300) K.Then, the fusion of the studied compound was observed.

Thermodynamic Characteristics of Fusion and the Purity Determination
The enthalpy of fusion ∆ fus H • = (52.79± 0.28) kJ mol −1 of the dicationic ionic liquid [C 4 (MIm) 2 ][NTf 2 ] 2 was determined using the calorimetric method of continuous energy input.The obtained results are given in Table 2.
cal dT is the energy supplied to heat the empty calorimeter (C cal is the heat capacity of the calorimeter); dT Are the energies supplied to heat the studied sample in crystalline and liquid states, respectively (C • p (cr) and C • p (liq)) the heat capacities of crystalline and liquid states of ionic liquid, respectively)?The sample mass was (0.56495 ± 0.00001) g.The enthalpy of fusion ∆ fus H • was calculated by the following equation: The mole fraction of impurities in the studied sample (x 2 ) and the triple point temperature (T tp ) of DIL were determined by the fractional melting experiment (from the calorimetric study of the reciprocal fractions of the sample melted, F −1 , as a function of the equilibrium fusion temperature, T • F ) [18].In other words, at each T • F temperature, the fraction F of the area under the calorimetric melting peak is evaluated.The obtained results are listed in Table 3 and are shown in Figure 3.It can be seen that the corresponding dependence T°F vs. F −1 is a straight line.It is well described by the Rossini Equation ( 4): where It can be seen that the corresponding dependence T • F vs. F −1 is a straight line.It is well described by the Rossini Equation ( 4): where T • 0 is the triple point temperature of the absolutely pure compound, and T where 2 was calculated using Equation ( 6): Thus, the standard thermodynamic characteristics of fusion of [C 4 (MIm) 2 ][NTf 2 ] 2 are T • fus = (337.88± 0.01) K, ∆ fus H • = (52.79± 0.28) kJ mol −1 , and ∆ fus S • = (156.2± 1.7) J K −1 mol −1 , where the corresponding uncertainties are standard deviations of the mean.
The results of the present work were compared with the literature data [19][20][21][22][23].It was confirmed that the T fus values of the dicationic ILs are substantially higher than those of the monocationic ILs with the same anion [NTf 2 ].Thus, the dicationic ILs seem more suitable for applications at high-temperature conditions than the corresponding monocationic ILs.Earlier, the temperature and the enthalpy of fusion of geminal dicationic ionic liquid [C 4 (MIm) 2 ][NTf 2 ] 2 were determined by the authors of [22] using differential scanning calorimetry (DSC).The melting point measured by DSC is reported as 329.2K [22].This value belongs to the temperature interval of the revealed phase transition.In addition, the value of Tm for dicationic ionic liquid [C 4 (MIm) 2 ][NTf 2 ] 2 is equal to (332.5 ± 0.7) K in accordance with the data from [19].The authors of [19] also performed DSC measurements with a heating rate of 10 K min −1 to determine the melting temperature of the above IL.In our work, the value of T • fus = (337.88± 0.01) K was determined as the end temperature in the range of fusion by precise adiabatic calorimetry under equilibrium conditions.Therefore, in comparing the literature values [19,22] with those resulting from our study, a close agreement could not be expected.Moreover, we note that no details of DSC experiments and the evaluation of T fus are provided in [19,22].With regard to the enthalpy of fusion, admittedly, a rather large discrepancy is found between our value, (52.79 ± 0.28) kJ mol −1 , and the value reported in [22] (23.6 kJ mol −1 ).The reason for this disagreement is difficult to understand.However, we note that the value of ∆ fus H [22] seems anomalously low when compared with that of the monocationic counterpart (EMImNTf 2 ), which was reported as (21.89 ± 0.03) kJ mol −1 .For the sake of comparison, it can be noted that the ∆ fus H values for the corresponding bromide compounds are 43.98 kJ mol −1 [22] and (18.26 ± 0.12) kJ mol −1 [23], for the dicationic and monocationic compounds, respectively.

Standard Thermodynamic Functions
The standard thermodynamic functions of [C 4 (MIm) 2 ][NTf 2 ] 2 listed in Table 4 were calculated from the C p values in the temperature range of 0-350 K.In order to determine the standard molar thermodynamic functions of [C 4 (MIm) 2 ][NTf 2 ] 2 , the Debye law [24] was used to extrapolate the low-temperature heat capacity from 6.5 K to 0: where n is the number of degrees of freedom, D n = n z n z 0 x n exp(x)−1 dx represents the Debye function, and Θ D is the Debye characteristic temperature.In Equation ( 7), the parameter n = 6, and Θ D = 38.8K is an adjustable coefficient.The experimental heat capacity values of the investigated DIL in the range of 6.5-10 K were described by Equation (7) using the above parameters with an error of 1.87%.The values of [H • (T) − H • (0)] and those of S • (T) were calculated in the temperature range 0-350 K by numerical integrations of the C p = f (T) and C p = f (lnT) values, respectively, while those of [G • (T) − H • (0)] were determined according to Equation ( 8):    The results previously reported that the heat capacity of DILs is scarce and limited to temperatures higher than room temperature.No previous investigation was reported from temperatures close to 0 K up.The most investigated series of DILs is that with the bromide ion, which was considered for thermal storage applications [22].One determination [22] is also available for [C 4 (MIm) 2 ][NTf 2 ] 2 , which is, to the best of our knowledge, the only C p value ever reported for a DIL with the NTf 2 anion before the present work.A direct comparison with our result is uncertain because the only value in [22] (1288 J K −1 mol −1 ) is given with no specification of the temperature.Assuming this value referred to the melting temperature (329.3K in [22]), it exceeds our result by more than 20%.The few data available to date allow for some insight into the dependence of the heat capacity on the nature of the anionic portion.According to our results, the heat capacity of [C 4 (MIm) 2 ][NTf 2 ] 2 is much lower than that of other DILs with the [C 4 (MIm) 2 ] ++ cation and typical anions such as BF 4 -, Br -and PF 6 -, thus confirming the strong dependence of heat capacities from the anion.The observed C p trend, Br − ∼ = BF 4 − > PF 6 − > NTf 2 − , can be readily interpreted as due to the different capacity to form hydrogen bonds.For example, a large number of hydrogen bonds was found in the crystal structure of C 4 (MIm) 2 ]Br 2 [22], also accounting for high values of the melting temperature and fusion enthalpy of this compound.Interestingly, the above heat capacity order is reversed if the decomposition temperatures are considered.It is thus interesting to wonder how accurately the measured C p values for the liquid phase of [C 4 (MIm) 2 ][NTf 2 ] 2 could be predicted by a simple estimation procedure based on the C p of the corresponding monocationic compounds.From the structure shown in Figure 1, it comes natural to tentatively estimate the [25] corrected by the different contributions of the CH 3 and CH 2 groups.By using this correction the group contribution values reported by Zábranský and R ůžička [26], the estimated C p value of liquid [C 4 (MIm) 2 ][NTf 2 ] 2 at the melting point (C p (est) = 992.0J K −1 mol −1 at T fus ) agrees fairly well (2.0%) with the experimental values reported in Table 2 (C p (exp) = 1012 J K −1 mol −1 ).If confirmed by further measurements, this simple procedure would allow obtaining a potentially useful, albeit rough, estimate of C p for DILs which no experimental value is available.

Materials and Methods
The structural formula of 1,4-bis(3-methylimidazolium-1-yl)butane bis(trifluoromethyl sulfonyl)imide ([C 4 (MIm) 2 ][NTf 2 ] 2 ) is presented in Figure 1 with n = 4.The synthesis and structural characterization of the studied dicationic ionic compound and of its bromide precursor has been carried out according to the procedure reported below (Sections 3.1 and 3.2).The benchmark compound [C 4 MIm][NTf 2 ] and lithium bis(trifluoromethylsulfonyl)imide Li[NTf 2 ] were purchased by Sigma-Aldrich (purity > 99.0% is provided by the supplier) and used as such.The information for the studied dicationic ionic liquid [C 4 (MIm) 2 ][NTf 2 ] 2 and the used reagents are listed in Table 5.The standard atomic masses recommended by the IUPAC Commission [27] were used to calculate the molar mass of the tested compound (M(C 16 H 20 F 12 N 6 O 8 S 4 ) = 780.56g mol −1 ).C/min under inert gas atmosphere), and it resulted in being below the detection limit of the instrument for both compounds (Figure S4, Supplementary Material).The mole fraction purity of the studied DIL was determined by the fractional melting technique in an adiabatic calorimeter to be 0.9903.Thus, it can be claimed that the purity of the synthesized DIL is high and meets the requirements of testing its thermodynamic properties.
The provided results of the NMR analysis (Figure S6, Supplementary Material) are in agreement with the literature data [16].

Heat Capacity Experiments
The heat capacity of dicationic ionic liquid [C 4 (MIm) 2 ][NTf 2 ] 2 has been measured over the range from T = (6 to 350) K using a precise automatic BCT-3 adiabatic calorimeter.The calorimeter was manufactured by "Termis" joint-stock company (Moscow region, Russia).Its design and the operation procedure were described in detail elsewhere [28].A miniature rhodium-iron resistance thermometer was calibrated on the basis of ITS-90 [29] and used for the temperature measurements during the calorimetric experiments.More detailed information about the thermometer calibration is published elsewhere [30,31].The sensitivity of the thermometric circuit was 0.001 K. Liquid helium and nitrogen were used as cooling agents.
The measurements were performed at p 298 (He) = (4 ± 1) kPa in the calorimetric cell with the studied substance (dry helium used as the thermal exchange gas).A high vacuum inside the container was kept by means of cryosorption provided with an efficient charcoal getter.The mass of the sample loaded in a thin-walled cylindrical titanium ampoule of the BCT-3 device was (0.56495 ± 0.00001) g.After assembling, the measuring system was cooled in the Dewar vessel with liquid nitrogen.When the measurements were performed below 80 K, liquid helium was used.The studied sample was first measured in the liquid nitrogen region, followed by measurements in the liquid helium with overlapping experimental temperature intervals.
The calorimeter reliability was verified by measuring the heat capacities of the reference samples, namely high-purity copper (mass fraction 0.99999) [32], synthetic corundum α-Al 2 O 3 (mass fraction 0.99993) [33], chromatographically pure n-heptane (mole fraction 0.99997) [34], and benzoic acid (mole fraction 0.99997) [35].The test of the calorimeter revealed the combined expanded relative uncertainty of the experimentally determined heat capacity U c,r (C p ) = 0.02 in the range T = (6-15) K, U c,r (C p ) = 0.005 for T = (15-40) K, U c,r (C p ) = 0.002 in the interval T = (40-350) K.The temperature and enthalpy of the phase transformations were determined with the standard uncertainty u(T tr ) = 0.01 K and the combined relative expanded uncertainty U c,r (∆ tr H) = 0.008 and U c,r (∆ tr S) = 0.011, respectively.The reported uncertainties correspond to the 0.95 confidence level (k ≈ 2).
Note that the time required for the calorimeter to reach the equilibrium temperature was determined experimentally.These values are 40 min in the phase transition region (the equilibrium period) and 15 min in all other temperature intervals.When the duration decreases, the equilibrium is failed in the system.The heat capacity of the sample varied from (20 to 40)% of the total heat capacity of the (calorimetric ampoule + substance) system over the range T = (6-350) K.

Conclusions
This study reports the original results of the calorimetric study on 1,4-bis(3methylimidazolium-1-yl)butane bis(trifluoromethylsulfonyl)imide dicationic ionic compound ([C 4 (MIm) 2 ][NTf 2 ] 2 ).In particular, the heat capacity of this substance was measured for the first time in the temperature range of 6-350 K by precise adiabatic calorimetry.The thermodynamic characteristics of fusion were determined by the fractional melting experiments and the calorimetric method of continuous energy input.The melting temperature of [C 4 (MIm) 2 ][NTf 2 ] 2 was found to be (337.88± 0.01) K, a value almost 70 K higher than that of the corresponding monocationic IL with a methyl and a butyl substituent on the imidazolium ring (
[C4(MIm)2][NTf2]2.The Cp values of three experimental runs for [C4MIm][NTf2] are compared in Figure S1 (Supplementary Material) with those available in the literature [15].A very good agreement was found between the experimental and the literature values (Figure S2, Supplementary Material), thus confirming that reliable heat capacity values may also be expected for [C4(MIm)2][NTf2]2.The experimental Cp values of [C4(MIm)2][NTf2]2 were determined in the range of 6-350 K, and the plot of the fitted values (Cp vs. T) are shown in Table 1 and Figure 2, respectively.The experimental Cp values were fitted in all the temperature regions where any transformations are absent according to the following polynomial Equations (1)-(3):

1
The standard uncertainty for temperature u(T) = 0.01 K in the interval of T = (6.52 to 350.12) K in Series 1-4.The combined expanded relative uncertainty for the heat capacity U c,r (C p ) = 0.02, 0.005, and 0.002 in the intervals of T = (6.52 to 15.27) K, T = (15.73 to 41.21) K, T = (42.84 to 350.12) K in Series 1-4, respectively.The reported uncertainties correspond to the 0.95 confidence level (k ≈ 2).Series 1: the C p values correspond to the crystalline state.Series 2: the C p values correspond to the crystalline state (T = (83.12-307.81)K) and the liquid state (T = (336.21-342.21)K); the C p values in brackets correspond to an apparent heat capacity in the interval of fusion.Series 3: the C p values correspond to the supercooled state (T = (316.69-335.42)K) and the liquid state (T = (338.21-350.12)K. Series 4: fractional melting experiment.Molecules 2024, 29, 4180 3 of 13 lnCp = ΣAi • ln(T/30) i , (1)

Figure 2 .
Figure 2. The heat capacity of [C 4 (MIm) 2 ][NTf 2 ] 2 in the temperature range 6-350 K: T fus is the temperature of fusion; ABF-crystalline state; DE-liquid state; DD'-supercooled liquid state (colored circles); BCC'D-an apparent heat capacity in the interval of fusion.

Table 1 .
The

Table 1 .
The experimental molar heat capacity
H • are the first and the second cryoscopic constants, respectively; ∆C • p (T • fus ) is the heat capacity increase at the fusion of [C 4 (MIm) 2 ][NTf 2 ] 2 .The mole fraction of impurities in the studied DIL is equal to 0.0097.The entropy of fusion